David Miliband has re-entered the debate about how to put Labour back in government, warning his brother that he will not win the keys to Downing Street by disavowing New Labour, relying too much on working-class votes, or by simply waiting for David Cameron to fail.

In a joint article for TheObserver with shadow foreign secretary Douglas Alexander, written from the Democrat convention in Charlotte, North Carolina, the two men say Labour needs to show it is on the side of prosperous middle-class voters as well its working-class base.

Urging the Labour leader to learn lessons from US politics, where they say President Obama is moving the Democrats on from the years of Bill Clinton without disavowing his legacy, they argue that Ed Miliband should not disregard the lessons from his party's recent past. Obama and Clinton sealed their political alliance with a bear hug at the Democratic convention last week.

They also say Labour, as the Democrats have done, must show it is committed to reform of the state, as well as reform of the markets – and to economic prudence in the medium term following a burst of Keynesian stimulus advocated by the shadow chancellor, Ed Balls.

Their intervention reflects unease on the Blairite wing of the party that the Labour leader is shifting too far left, out of a belief that the financial crisis has created a fundamental change in public attitudes towards rampant wealth creation and unregulated markets. They argue the message has to remain unequivocally in favour of the market economy.

"It is true that there is not a single successful economy today where government does not play a vital role in driving forward market economies and standing up for the public interest," they write. "But there is another truth after the financial crisis: that government is on trial as well as the markets."

Drawing lessons from the race for the White House ahead of presidential elections in November, they write: "The Democrats, just like Labour, cannot rely only on the New Deal coalition of the organised working class. So they are supplementing that coalition by embracing the rising classes and groups in society – notably Latinos, but also middle income women who are the one group in the population, outside the elite, whose income has gone up in the last 30 years.

"It helps the Democrats that the Republicans are so aggressively wrong on issues of gay rights, women's rights and minority rights. We won't have that luxury in the same way here – unless the Tories really lose it culturally as well as economically – so we have to find new ways to connect our politics with the small businesswoman in Ipswich, the GP in Fleetwood, the personal trainer in Gloucester."

Further trouble looms for Ed Miliband as the political conference season gets under way with the TUC congress in Brighton. Several unions, including Labour's biggest financial backer Unite, are calling for more co-ordinated industrial action in the public sector over pay cuts.

In an interview with the Observer today, the general secretary elect of the TUC, Frances O'Grady, – the first woman ever to take on the post – says the TUC will back co-ordinated strikes if delegates support them. "If members vote for it then the TUC will stand ready to support them," she said. Throwing her support behind Len McCluskey, the general secretary of Unite, who is pushing for an escalation of strikes in the runup to the next election, O'Grady said while the unions shared values with Labour, her duty was to union members and not Ed Miliband. "Ed Miliband will be leading a political party. I will be leading a trade union movement," she said.

Controversially, David Miliband and Alexander hint that they would like to see Labour relying less on union money as they call for fundamental reform of party funding.

"In Britain there is a structural imperative for Labour to take down the influence of money in politics – not just as a high-minded recognition of voter concern, but out of sheer self interest," they write.

"At the moment, party funding reform is going nowhere. So this autumn Labour should again reach out to the Liberal Democrats with the aim of working together to get big money out of politics. Some parts of the current system help us, but overall the Tories are the party that stands to benefit most from stalemate."

A senior Labour source said: "Ed Miliband agrees with this analysis. Like President Clinton and President Obama, he believes the success of progressive politics lies in bringing people together to make markets work and create a more responsible capitalism.

"He believes that in the face of increasing Tory divisiveness and division, Labour is the party that brings the country together and unites it. He believes that David Cameron has made a big mistake in shifting away from the political centre ground and seeking to blame people for the problems of the country."